Question 4.DE.8: Air enters axially in a centrifugal compressor at a stagnati......
Air enters axially in a centrifugal compressor at a stagnation temperature of 20°C and is compressed from 1 to 4.5 bars. The impeller has 19 radial vanes and rotates at 17,000 rpm. Isentropic efficiency of the compressor is 0.84 and the work input factor is 1.04. Determine the overall diameter of the impeller and the power required to drive the compressor when the mass flow is 2.5 kg/s.
Since the vanes are radial, using the Stanitz formula to find the slip factor:
σ = 1 – \frac{0.63\pi} {n} = 1 – \frac{0.63\pi}{19} = 0.8958
The overall pressure ratio
\frac{P_{03}} {P_{01}} = \left[1 + \frac{η_cσψU_2^2}{C_pT_{01}}\right]^{γ/(γ-1)} , or 4.5
= \left[1 + \frac{(0.84)(0.8958)(1.04)(U^2_2)}{(1005)(290)}\right]^{3.5} , so U_2 = 449.9 m/s
The impeller diameter, D = \frac{60U_2} {\pi N} = \frac{(60)(449.9)}{\pi (17,000)} = 0.5053 m = 50.53 cm.
The work done on the air W = \frac{ψσU_2^2}{1000} = \frac{(0.8958)(1.04)(449.9^2)} {1000} = 188.57 kJ/kg
Power required to drive the compressor: P = \dot{m} W = (2.5)(188.57) = 471.43 kW